The Quasistationary Approximation Ampere’s Law + Faraday’s Law Application in: electrical...

The Quasistationary Approximation

Ampere’s Law + Faraday’s Law

Application in: electrical engineering, radio, TV, audio, …

time x velocity of light >> size

Inductance

inductive coupling betweentwo circuits

dt

dIM

dt

dIM

MIMI

ddM

21

12

2112

21

210

4

EE

rr

ll

Example 7.10

Find the mutual inductance.

Mutual inductance?

Self-inductance

The change of B induces a back-emf in the loop that generates the magnetic field:self-induction.

dt

dILE

L self-inductance

Unit: Henry 1H=1Vs/A

Example 7.11

Self-inductance of a toroidalcoil with recangular cross section,which carries a total of N turns.

The transformer

VIP

RIP

user

line

2

Low current and high voltage used.

Long distant line Distribution within a neighborhood

Example 7.12

oq

q

Oscillator Circuits

C

o

t

o teqtq

22)( 2

o

t

o

do

eqtq

22)( 2

odo

t

o teqtq

2)cos()( 2

Driven Oscillator

C

AC

Driven oscillator with differentinitial conditions.

Resonance

Self-excited circuit

Radio tubes

1930

A shipboard radio, circa 1920. Exposed at the operator’s left are the inductance coils and capacitor plates of the tuning circuit.

transistors microchip

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/accircon.html#c1

Multi-loop Circuits

Kirchhoff’s rules:

1. When any closed-circuit loop is traversed, the algebraic sum of the changes in the potential must be equal to zero.

2. At any junction point in a circuit where the current can divide, the sum of the currents into the junction must equal the sum of the currents out of the junction.

DC circuit

Find the currents.

Find the currents.

AC circuit

3I2I